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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 172480w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 172480.ci2 | 172480w1 | \([0, -1, 0, 495, 3025]\) | \(16674224/15125\) | \(-12142592000\) | \([]\) | \(110592\) | \(0.62234\) | \(\Gamma_0(N)\)-optimal |
| 172480.ci1 | 172480w2 | \([0, -1, 0, -5105, -188495]\) | \(-18330740176/8857805\) | \(-7111187578880\) | \([]\) | \(331776\) | \(1.1716\) |
Rank
sage: E.rank()
The elliptic curves in class 172480w have rank \(2\).
Complex multiplication
The elliptic curves in class 172480w do not have complex multiplication.Modular form 172480.2.a.w
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
